In a Transmission Electron Microscope (TEM) a beam of electrons produced by an electron source is formed into a parallel beam of electrons illuminating the sample. The sample is very thin, so that part of the electrons pass through the sample and part of the electrons are absorbed in the sample. Some of the electrons are scattered in the sample so that they exit the sample under a different angle than under which they enter the sample, while others pass through the sample without scattering. By imaging the sample on a detector, such as a fluorescent screen or a CCD camera, intensity variations result in the image plane. The intensity fluctuations are in part due to the absorption of electrons by the sample, and in part to interference between scattered and unscattered electrons. The latter mechanism is especially important when observing samples in which little electrons are absorbed, e.g. low-Z materials such as biological tissues.
The contrast of the image resulting from electrons interfering with each other can, for parallel illumination, be explained as follows:
A parallel illumination can be described in Fourier space as a distribution δ(G) where δ denotes the well-known Dirac delta function which is only non-zero at G=0, and G denotes spatial frequency. The scattering of the incoming beam is described by the specimen function φ(G). The beam Ψ0(G) immediately after the specimen becomesΨ0(G)=δ(G)−iφ(G)  [1]The imaging system, and in particular the objective lens of the TEM, aberrates this wave toΨ(G)=δ(G)−iφ(G)exp[2πiχ(G)]  [2]where χ(G) is the aberration function which depends on parameters like defocus and spherical aberration. The intensity at the detector is equal to the convolution of Ψ(G) with its complex conjugate Ψ(G)*,|(G)=Ψ(G)*Ψ*(G)  [3a]This can be written as|(G)=δ(G)−iφ(G)exp[2πiχ(G)]+iφ*(−G)exp[−2πiχ(−G)]+φ(G)exp[2πiχ(G)]*φ*(−G)exp[−2πiχ(−G)]  [3b]As in Fourier space both frequencies G and −G are present, and since φ(x) is a real function, φ*(−G) can be replaced with φ(G).φ*(−G)=φ(G)  [4]Similarly, since χ(G) is even in G, χ(−G) can be replaced with χ(G).χ(G)=χ(−G)  [5]The expression for the intensity simplifies to|(G)=δ(G)−2φ(G)sin [2πiχ(G)]+φ(G)exp[2πiχ(G)]*φ(G)exp[−2πiχ(G)]  [6]The factor sin [2πiχ(G)] is called the Contrast Transfer Function (CTF):CTF(G)=sin [2πiχ(G)]  [7]The term quadratic in φ(G) is small and is usually neglected.
Objects with a specific spatial frequency scatter the beam over a specific angle, the scattering angle being proportional to the spatial frequency. For low spatial frequencies the scattering angle is close to zero and the contrast is close to zero as χ(G) and consequently the CTF is almost zero. For higher spatial frequencies the contrast fluctuates due to the positive and a negative values for the CTF, depending on the spatial frequency. As the CTF is close to zero for low spatial frequencies, large structure cannot be resolved in the image.
In 1947 Boersch described that the introduction of a phase plate would result in a CTF where low spatial frequencies show a maximum, and large structures can thus be imaged, see “Über die Kontraste von Atomen im Elektronenmikroskop”, H. Boersch, Z. Naturforschung 2A (1947), p. 615-633. Recently such phase plates have successfully been introduced in TEM's.
A phase plate is a structure that is placed in a plane where the beam illuminating the sample, after having passed through the sample, is focused to a spot by the so-named objective lens.
It is noted that a phase plate can also be placed in a plane that is an image of the plane where the objective lens focuses the beam to a spot.
Usually, the illuminating beam is a parallel beam, and then the plane where the beam is focused to a spot is the back-focal plane of the objective lens. If the illuminating beam is not a parallel beam, but close to parallel, then this plane is close to the back-focal plane of the objective lens or close to an image of said plane. In the plane of the phase plate all unscattered electrons are focused in one point, while scattered electrons are imaged at other positions. The phase plate causes a phase shift θ between scattered and unscattered electrons. Therefore equation [2] is modified toΨ(G)=δ(G)−iφ(G)exp[2πiχ(G)+θ]  [8]and thus equation [7] toCTF(G)=sin [2πiχ(G)+θ]  [9]By choosing θ=π/2 (or more general: θ=π/2+2nπ, with n an integer), this reduces toCTF(G)=cos [2πiχ(G)]  [10]thereby converting the sine-like behaviour of the CTF to a cosine-like behaviour. It is noted that a phase shift of θ=−π/2 also causes a cosine-like behaviour of the CTF. It is further noted that a marked improvement of the contrast may also occur for phase shifts other than θ=π/2+nπ.
For a more detailed derivation of the formulae the reader is referred to “High-resolution electron microscopy”, J. C. H. Spence, 3rd edition (2003), ISBN 0198509154, more specifically to paragraph 3.4 and chapter 4.
In a so-named Boersch phase plate such a phase shift is caused by temporary accelerating or decelerating the unscattered electrons.
A Boersch phase plate must have a very small diameter to allow (most of the) scattered electrons to pass without intercepting these scattered electrons by the physical structure of the phase plate. The manufacturing of such a phase plate is described in e.g. U.S. Pat. No. 5,814,815 to Hitachi.
The known phase plate comprises a grounded ring-like structure with an inner electrode, thus resembling a miniature electrostatic Einzellens. The electrons passing through the phase plate are temporarily accelerated or decelerated. By a proper choice of the voltage on the inner electrode the phase shift θ of the electrons is e.g. plus or minus π/2. The electrons that are passing outside the miniature lens do not experience the phase shift. By positioning the phase plate in a plane where the beam illuminating the sample is focused to a point and centering it round the axis of the objective lens, the unscattered electrons experience the phase shift, while all electrons that are scattered pass outside the phase plate and thus do not experience the phase shift.
A problem of the known phase plate is that the central structure intercepts electrons, thereby blocking electrons scattered over a small angle. These electrons are necessary to image structures with a low spatial frequency. Large structures can thus not be imaged with such a phase plate.
It is noted that any scattered electrons that also pass through the phase plate, because they are scattered over a very small angle, will experience the same phase shift as the unscattered electrons and can thus not interfere with the unscattered electrons to form a high contrast image.
A disadvantage of the known phase plate is that large structures can not be imaged as the scattered electrons carrying the information with low spatial resolution are either blocked by the physical structure of the phase plate or experience the same phase shift as the unscattered electrons. This makes it difficult to navigate to points of interest in the sample, or to observe the position of a high resolution feature, such as a lipid bi-layer, in a large feature, such as a cell.
It is noted that another type of Boersch phase plate is described in International Application WO2006/017252 to Glaeser. This phase plate comprises a central ring electrode surrounded by a grounded ring electrode. Herewith an electric field can be generated on the axis, thereby accelerating or decelerating the unscattered electrons, while the grounded electrode acts as a shield so that scattered electrons do not experience a phase shift. The disadvantages mentioned for the phase plate of U.S. Pat. No. 5,814,815 are equably applicable.